Monday, August 26th

1. Solve for x and Y

Warm Up

2. Solve for Z

HOMEWORKANSWERS

Any polygon with four sides is a quadrilateral. However, some

quadrilaterals have special properties.

These special quadrilaterals are given

their own names.

Opposite sides of a quadrilateral do not share a vertex. Opposite angles do not share a side.

Helpful Hint

Parallelograms

A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol .

I. The Properties of Parallelograms

1. Opposite sides are congruent (AB=DC)

2. Opposite angles are congruent (D=B)

3. Consecutive angles are supplementary (A+D=180)

4. If one angle is right, then all angles are right.

5. The diagonals of a parallelogram bisect each other.

6. Each diagonal of a parallelogram separates it into two congruent triangles.

A B

CD

II. Finding Missing

Angles and Lengths

Example 1 Part A

Def. of segs.

Substitute 74 for DE.

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF.

CF = DE

CF = 74 mm

opp. sides

Substitute 42 for mFCD.

Example 1 Part B

Subtract 42 from both sides.

mEFC + mFCD = 180°

mEFC + 42 = 180

mEFC = 138°

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC.

cons. s supp.

In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure.

1. PW 2. mPNW

18 144°

#2 You Try!

III. Using Algebra

Example 1A

WXYZ is a parallelogram. Find YZ.

Def. of segs.

Substitute the given values.

Subtract 6a from both sides and add 4 to both sides.

Divide both sides by 2.

YZ = XW

8a – 4 = 6a + 10

2a = 14

a = 7

YZ = 8a – 4 = 8(7) – 4 = 52

opp. s

Example 1B

WXYZ is a parallelogram. Find mZ .

Divide by 27.

Add 9 to both sides.

Combine like terms.

Substitute the given values.

mZ + mW = 180°

(9b + 2) + (18b – 11) = 180

27b – 9 = 180

27b = 189

b = 7

Answer: mZ = (9b + 2)° = [9(7) + 2]° = 65°

cons. s supp.

You Try! #2 A

EFGH is a parallelogram.Find JG.

Substitute.

Simplify.

EJ = JG3w = w + 8

2w = 8

w = 4 Divide both sides by 2.

JG = w + 8 = 4 + 8 = 12

Def. of segs.

diags. bisect each other.

#2 Part B

EFGH is a parallelogram.Find FH.

Substitute.

Simplify.

FJ = JH

4z – 9 = 2z

2z = 9

z = 4.5 Divide both sides by 2.

Def. of segs.

FH = (4z – 9) + (2z) = 4(4.5) – 9 + 2(4.5) = 18

diags. bisect each other.

QRST is a parallelogram. Find each measure.

2. TQ 3. mT

28 71°

#3 You Try!